(a) A rectangular block has the dimensions ? ? w ? h . When a battery with a vol

Question

(a) A rectangular block has the dimensions ? ? w ? h. When a battery with a voltage V is connected across the end faces as shown in the left figure above, a current I1 flows through the circuit. If the same battery is connected across the top and bottom faces of the block as shown in the right figure, what is the current I2 that flows through the circuit? Give your answer in terms of I1. (Use the following as necessary: ?, w, h, I1)

I2 =

(b) Suppose ? = 3.80 cm, w = 2.2 cm, and h = 2.00 cm; the battery voltage is 1.5 V and I1 = 3.30 A, determine the value of I2.
         _________A

Explanation / Answer

part A)

as the current in the circuit is given as

using Ohm's law

I1 = V * /R

I1 = V/(p * l/(w*h))

I1 = V * w*h/(p *l)

for the current in I2

I2 = V/(p * h/(l * w))

I2 = V * l * w/(p*h)

b)

putting in I1

I1 = V * w*h/(p *l)

3.3 = 1.5 * 0.022 * 0.02/(p * 0.038)

solving for p

p = 5.263 *10^-3 Ohm.m

putting in I2

I2 = 1.5 * 0.038 * 0.022/(5.263 *10^-3 * 0.02)

I2 = 11.91 A

the current I2 is 11.91 A

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